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  1. Nosotros trabajamos (we work)
  2. Nosotros podemos trabajar (we can work)

Different verb conjugation for "trabajar" because of the word "podemos". Please can someone explain how to arrive at "trabajar" in the second example and under what circumstances I have to revert to the infinitive like this? "We" remains the performing component in the second example so I can't wrap my brain around why the infinitive is used rather than "nosotros podemos trabajamos".

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    Note that it is similar in English: he works, he can work – rsanchez Jan 4 '19 at 14:42
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In English it's not so noticeable, but the fact is that even in English, you conjugate one verb and leave one verb as an infinitive. To convince you of this, consider this sentence:

She wants to study economics. | Ella quiere estudiar la economía.

"Want" gets conjugated, but "study" doesn't.

(There is a "to" here that we don't see in your example, "We can work," but that's because "can" is a modal, and doesn't need the "to." That's just a quirk of English.)

Here are some more sentences in Spanish to help you get used to this pattern:

  • ¡Deja de fastidiarme ya!

  • Debemos trabajar más rápido.

  • ¿Puedes traer la sal, por favor?

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The first one indicates and action or a place, for example

We work at the Central Bank

We work as tv actors

The second one is used to describe a possibility to do something, for example

We can work for hours building blocks

We can work on your TV show as hosts tomorrow

So I do recommend you to distinguish what do you need to transmit to others, to organize in a better way these two possible scenarios

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In your second example we have a perífrasis verbal.

According to the DRAE

perífrasis verbal

  1. f. Gram. Unidad predicativa constituida generalmente por un verbo auxiliar en forma personal y un verbo auxiliado en forma no personal

[English: Predicative unit generally formed by an auxiliary verb in personal form and a main verb in non-personal form.

Notice that I have "translated" auxiliado by main, applying the definition of auxiliary that appears in the Cambridge Dictionary

auxiliary verb: a verb that gives grammatical information not given by the main verb of a sentence

The main verb of a "perífrasis verbal" is always in non-personal form meaning that it's an infinitive, a gerund or a participle. It's always the auxiliary verb, poder in your case, the one that applies person, number and genre.

Notice that the same occurs in English with the verb can that you quoted. This verb is a modal verb and

Modal verbs (can, could, may, might, will, shall, would, should and must) are followed by a bare infinitive source

More info [in Spanish] about "perífrasis verbales" here.

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